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Lie Algebroid Invariants for Subgeometry
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the infinitesimal invariants of an immersed submanifold $\Sigma $ of a Klein geometry $M\cong G/H$, and in particular an invariant filtration of Lie algebroids over $\Sigma $. The invariants are derived from the logarithmic derivative of the immersion of $\Sigma $ into $M$, a complete invariant introduced in the companion article, A characterization of smooth maps into a homogeneous space. Applications of the Lie algebroid approach to subgeometry include a new interpretation of Cartan's method of moving frames and a novel proof of the fundamental theorem of hypersurfaces in Euclidean, elliptic and hyperbolic geometry.
Keywords: subgeometry; Lie algebroids; Cartan geometry; Klein geometry; differential invariants. 
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     author = {Anthony D. Blaom},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a61/}
}
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Anthony D. Blaom. Lie Algebroid Invariants for Subgeometry. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a61/

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